When a company says they keep the info provided on file, that usually exactly what they're doing, if LE was to question the age of a person with a ad, with that verbiage they are going to show what they have to prove it.
They have nothing to lose by keeping it and a lot to lose by not keeping it.
Remember they are not in business to keep you from running afoul of the law or obstructing the law, they have to stay above board. they don't post your RW info, but if LE orders them for it how else will they be able to prove you're of age without it.